@ciavelillse,
First, she's not your GF. Yet. Cool it with the GF talk. You don't know her yet.
You MUST go up to her and say hello. Do this with a friend and be very nice. Ask her about a class or school event. "Hey, are you girls going to the game?"
That's about it. If you can't go up to a girl, then you are not ready for a GF.